Problem: Solve for $x$. Enter the solutions from least to greatest. $(-5x +4)(x -3)=0$ $\text{lesser }x = $
For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(-5x +4)(x -3)=0$. So either $(-5x +4)=0$ or $(x -3)=0$ : $\begin{aligned} (1)&&-5x +4&=0 \\\\ &&-5x&=-4 \\\\ &&x&=\dfrac{4}{5} \end{aligned}$ $\begin{aligned} (2)&&x -3&=0 \\\\ &&x&=3 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= \dfrac{4}{5} \\\\ \text{greater } x &= 3 \end{aligned}$